(\partial)/(\partial y)(ln(x-7y))

解

\frac{\partial}{\partial y} (ln (x - 7 y))

- \frac{7}{x - 7 y}

解答ステップ

\frac{\partial}{\partial y} (ln (x - 7 y))

x

を定数として扱う

連鎖法則を適用:

\frac{1}{x - 7 y} \frac{\partial}{\partial y} (x - 7 y)

= \frac{1}{x - 7 y} \frac{\partial}{\partial y} (x - 7 y)

\frac{\partial}{\partial y} (x - 7 y) = - 7

= \frac{1}{x - 7 y} (- 7)

簡素化

\frac{1}{x - 7 y} (- 7) : - \frac{7}{x - 7 y}

= - \frac{7}{x - 7 y}